A barrel can only impart the twist it has to the bullet (twists per inch or travel). Increasing the powder charge will generally increase the velocity, but will not change the number of rotations the bullet makes as it travels over a given distance. That is "programmed" by the barrel. If you shoot a 50 grain load your bullet will rotate within the barrel a given number of times. Does that change with a 100 grain load? No, the only thing that changed is the time it took to travel the length of the barrel. The flight time to the target will also be reduced (though a very small amount within the range of hunting loads), so the bullet will make the same number of rotations in minimally less time. If you want to look at that as more RPM, ok, but it is not more rotations between the muzzle and the target.

As stated above, longer projectiles require more twist than shorter ones of equal diameter.

I'm no physicist, but I can't think of any reason a perfectly round ball would be more or less stable with a change in twist rate, if all other things are equal. But, that's where the problem is, in all the other things that are not equal, like the ability of the patch to impart spin as pressures increase, barrel harmonics, the actual concentricity of the bullet and all the rest of the imperfect things in the shooting system.

So, with a given bullet and a given gun, there will be a charge that stabilizes the bullet optimally to overcome a high percentage of the imperfections in the system. Bullet stability may decrease above or improve below that optimal charge. A gun may also have more than one sweet spot for a given projectile.